Chaos and damping in the post-Newtonian description of spinning compact binaries

Abstract

Binary systems of rapidly spinning compact objects, such as black holes or neutron stars, are prime targets for gravitational wave astronomers. The dynamics of these systems can be very complicated due to spin-orbit and spin-spin couplings. Contradictory results have been presented as to the nature of the dynamics. Here we confirm that the dynamics---as described by the second post-Newtonian approximation to general relativity---is formally chaotic, despite claims to the contrary. When dissipation due to higher order radiation reaction terms is included, the chaos is damped. The damping time scale is found to be comparable to, but shorter than, the time scale that characterizes the chaotic behavior. This result suggests that the gravitational waveforms computed to 2.5 post-Newtonian order from spinning compact binaries will not suffer from sensitive dependence on initial conditions. If the post-Newtonian approximation at this order is an adequate description, then the waves can be detected using standard hierarchical matched filtering techniques. On the other hand, the competition between chaotic decoherence and radiation induced dissipation is close enough that the merger history does retain an imprint of the chaotic behavior. Moreover, the time scales are sufficiently close, and the post-Newtonian approximation is sufficiently crude, that we cannot rule out the possibility that chaotic effects play a role in real binary systems.